Neper
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The neper (symbol: Np) is a
logarithmic unit A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a ...
for
ratio In mathematics, a ratio shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ...
s of measurements of physical field and power quantities, such as
gain Gain or GAIN may refer to: Science and technology * Gain (electronics), an electronics and signal processing term * Antenna gain * Gain (laser), the amplification involved in laser emission * Gain (projection screens) * Information gain in de ...
and loss of electronic signals. The unit's name is derived from the name of
John Napier John Napier of Merchiston (; 1 February 1550 – 4 April 1617), nicknamed Marvellous Merchiston, was a Scottish landowner known as a mathematician, physicist, and astronomer. He was the 8th Laird of Merchiston. His Latinized name was Ioann ...
, the inventor of logarithms. As is the case for the
decibel The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a po ...
and bel, the neper is a unit defined in the
international standard international standard is a technical standard developed by one or more international standards organizations. International standards are available for consideration and use worldwide. The most prominent such organization is the International Or ...
ISO 80000 ISO 80000 or IEC 80000 is an international standard introducing the International System of Quantities (ISQ). It was developed and promulgated jointly by the International Organization for Standardization (ISO) and the International Electrote ...
. It is not part of the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
(SI), but is accepted for use alongside the SI.


Definition

Like the
decibel The decibel (symbol: dB) is a relative unit of measurement equal to one tenth of a bel (B). It expresses the ratio of two values of a power or root-power quantity on a logarithmic scale. Two signals whose levels differ by one decibel have a po ...
, the neper is a unit in a
logarithmic scale A logarithmic scale (or log scale) is a way of displaying numerical data over a very wide range of values in a compact way—typically the largest numbers in the data are hundreds or even thousands of times larger than the smallest numbers. Such a ...
. While the bel uses the decadic (base-10)
logarithm In mathematics, the logarithm is the inverse function to exponentiation. That means the logarithm of a number  to the base  is the exponent to which must be raised, to produce . For example, since , the ''logarithm base'' 10 o ...
to compute ratios, the neper uses the
natural logarithm The natural logarithm of a number is its logarithm to the base of the mathematical constant , which is an irrational and transcendental number approximately equal to . The natural logarithm of is generally written as , , or sometimes, if ...
, based on
Euler's number The number , also known as Euler's number, is a mathematical constant approximately equal to 2.71828 that can be characterized in many ways. It is the base of a logarithm, base of the natural logarithms. It is the Limit of a sequence, limit ...
(). The level a ratio of two signal amplitudes or root-power quantities, with the unit neper, is given by : L = \ln\frac\mathrm, where x_1 and x_2 are the signal amplitudes, and is the natural logarithm. The level of a ratio of two power quantities, with the unit neper, is given by : L = \frac \ln\frac\mathrm, where p_1 and p_2 are the signal powers. In the
International System of Quantities The International System of Quantities (ISQ) consists of the quantities used in physics and in modern science in general, starting with basic quantities such as length and mass, and the relationships between those quantities. This system underlie ...
, the neper is defined as .


Units

The neper is defined in terms of ratios of field quantities — also called ''root-power quantities'' — (for example,
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
or
current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...
amplitudes in electrical circuits, or
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and e ...
in
acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...
), whereas the decibel was originally defined in terms of
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
ratios. A power ratio 10 log ''r'' dB is equivalent to a field-quantity ratio 20 log ''r'' dB, since power in a linear system is proportional to the square (
Joule's laws Joule effect and Joule's law are any of several different physical effects discovered or characterized by English physicist James Prescott Joule. These physical effects are not the same, but all are frequently or occasionally referred to in the lite ...
) of the amplitude. Hence the decibel and the neper have a fixed ratio to each other: : 1\ \text = 20 \log_ e\ \text \approx \text and : 1\ \mathrm = \frac \ln(10)\ \mathrm \approx \text . The (voltage) level ratio is : \begin L & = 10 \log_ \frac & \text \\ & = 10 \log_ ^2 & \text \\ & = 20 \log_ \frac & \text \\ & = \ln \frac & \text. \\ \end Like the decibel, the neper is a dimensionless unit. The
International Telecommunication Union The International Telecommunication Union is a specialized agency of the United Nations responsible for many matters related to information and communication technologies. It was established on 17 May 1865 as the International Telegraph Unio ...
(ITU) recognizes both units. Only the neper is
coherent Coherence, coherency, or coherent may refer to the following: Physics * Coherence (physics), an ideal property of waves that enables stationary (i.e. temporally and spatially constant) interference * Coherence (units of measurement), a deri ...
with the SI.


Applications

The neper is a natural linear unit of
relative difference In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a ''standard'' or ''reference'' or ''starting'' v ...
, meaning in nepers (logarithmic units) relative differences add rather than multiply. This property is shared with logarithmic units in other bases, such as the bel. The derived units decineper (1 dNp = 0.1 neper) and centineper (1 cNp = 0.01 neper) are also used. The centineper for root-power quantities corresponds to a
log point In any quantitative science, the terms relative change and relative difference are used to compare two quantities while taking into account the "sizes" of the things being compared, i.e. dividing by a ''standard'' or ''reference'' or ''starting'' v ...
or log percentage, see '.


See also

*
Nat (unit) The natural unit of information (symbol: nat), sometimes also nit or nepit, is a unit of information, based on natural logarithms and powers of ''e'', rather than the powers of 2 and base 2 logarithms, which define the shannon. This unit is ...


References


Works

*


Further reading

* *


External links


What's a neper?Calculating transmission line losses
{{SI units Units of measurement Logarithmic scales of measurement